We call progressive paths and rushed paths two families of Dyck paths studied by Asinowski and Jelinek, which have the same enumerating sequence (OEIS entry A287709). We present a bijection proving this fact. Rushed paths turn out to be in bijection with one-sided trees, introduced by Durhuus and Unel, which have an asymptotic enumeration involving a stretched exponential. We conclude by presenting several other classes of related lattice paths and directed animals that may have similar asymptotic properties.

翻译：我们将Asinowski和Jelinek研究的两类Dyck路径分别称为渐进路径和急行路径，它们具有相同的计数序列（OEIS条目A287709）。我们通过一个双射证明了这一事实。急行路径与Durhuus和Unel引入的单侧树之间存在双射关系，该树类的渐近计数涉及拉伸指数。最后，我们给出了其他几类可能具有类似渐近性质的格路和有向动物。